360 degree potentiometer

I want to interface a arduino mechanically with an old style clock. I attached a potentiometer to one of the gears then realized that the potentiometer doesn't rotate 360 degrees. It must rotate 360 degrees since the gear only turns in one direction. Does anybody know the name of a device that will act as a 360 degree potentiometer?

Thanks

You can modify most potentiometers to rotate 360 degrees by removing the stop tabs. Some are easier than others.

Even when modified there will be a section that doesn't have any resistance.

Another possibility is to use a rotary encoder. There was some discussion on the board a week or so ago about them.